direct_and_inverse_variation.js

Khan.testExercise({"exercise":"direct_and_inverse_variation","problems":[{"seed":1333556995,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":2,"MULTIPLIER":"\\frac{1}{2}","STATEMENT":"<code style=\"display: none;\">m</code> varies directly with <code style=\"display: none;\">n</code>"},"solution":"m = \\frac{1}{2} \\cdot n","pass":true},{"seed":161225069,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":9,"MULTIPLIER_INVERSE":9,"MULTIPLIER":"\\frac{1}{9}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-325\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-326\" class=\"mrow\"><span id=\"MathJax-Span-327\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-47\" style=\"display: none;\">x</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-328\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-329\" class=\"mrow\"><span id=\"MathJax-Span-330\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-48\" style=\"display: none;\">y</code>"},"solution":"x = \\frac{1}{9} \\cdot y","pass":true},{"seed":54385394,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":2,"MULTIPLIER":"\\frac{1}{2}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-493\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-494\" class=\"mrow\"><span id=\"MathJax-Span-495\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-67\" style=\"display: none;\">m</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-496\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-497\" class=\"mrow\"><span id=\"MathJax-Span-498\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-68\" style=\"display: none;\">n</code>"},"solution":"m = \\frac{1}{2} \\cdot n","pass":true},{"seed":120553043,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":2,"MULTIPLIER":"\\frac{1}{2}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-661\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-662\" class=\"mrow\"><span id=\"MathJax-Span-663\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-87\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-664\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-665\" class=\"mrow\"><span id=\"MathJax-Span-666\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-88\" style=\"display: none;\">b</code> are in direct variation"},"solution":"a = \\frac{1}{2} \\cdot b","pass":true},{"seed":103667515,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":5,"MULTIPLIER_INVERSE":"\\frac{1}{5}","MULTIPLIER":5,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-829\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-830\" class=\"mrow\"><span id=\"MathJax-Span-831\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-107\" style=\"display: none;\">x</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-832\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-833\" class=\"mrow\"><span id=\"MathJax-Span-834\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-108\" style=\"display: none;\">y</code>"},"solution":"x = 5 \\cdot y","pass":true},{"seed":57605038,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":"\\frac{1}{6}","MULTIPLIER":6,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-985\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-986\" class=\"mrow\"><span id=\"MathJax-Span-987\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-127\" style=\"display: none;\">a</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-988\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-989\" class=\"mrow\"><span id=\"MathJax-Span-990\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-128\" style=\"display: none;\">b</code>"},"solution":"a = 6 \\cdot b","pass":true},{"seed":44671714,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":9,"MULTIPLIER_INVERSE":9,"MULTIPLIER":"\\frac{1}{9}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1141\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-1142\" class=\"mrow\"><span id=\"MathJax-Span-1143\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-147\" style=\"display: none;\">m</code> varies directly with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1144\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-1145\" class=\"mrow\"><span id=\"MathJax-Span-1146\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-148\" style=\"display: none;\">n</code>"},"solution":"m = \\frac{1}{9} \\cdot n","pass":true},{"seed":62002608,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":8,"MULTIPLIER":"\\frac{1}{8}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1309\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-1310\" class=\"mrow\"><span id=\"MathJax-Span-1311\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-167\" style=\"display: none;\">m</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1312\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-1313\" class=\"mrow\"><span id=\"MathJax-Span-1314\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-168\" style=\"display: none;\">n</code>"},"solution":"m = \\frac{1}{8} \\cdot n","pass":true},{"seed":69383217,"type":"direct-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":3,"MULTIPLIER":"\\frac{1}{3}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1477\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-1478\" class=\"mrow\"><span id=\"MathJax-Span-1479\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-187\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1480\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-1481\" class=\"mrow\"><span id=\"MathJax-Span-1482\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-188\" style=\"display: none;\">b</code> vary directly"},"solution":"a = \\frac{1}{3} \\cdot b","pass":true},{"seed":249089841,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":"\\frac{1}{3}","MULTIPLIER":3,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1969\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-1970\" class=\"mrow\"><span id=\"MathJax-Span-1971\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-255\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-1972\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-1973\" class=\"mrow\"><span id=\"MathJax-Span-1974\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-256\" style=\"display: none;\">b</code> are in direct variation"},"solution":"\\frac{a}{b} = 3","pass":true},{"seed":84994981,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":"\\frac{1}{4}","MULTIPLIER":4,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2125\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-2126\" class=\"mrow\"><span id=\"MathJax-Span-2127\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-279\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2128\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-2129\" class=\"mrow\"><span id=\"MathJax-Span-2130\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-280\" style=\"display: none;\">y</code> vary directly"},"solution":"\\frac{x}{y} = 4","pass":true},{"seed":61025804,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":2,"MULTIPLIER":"\\frac{1}{2}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2281\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2282\" class=\"mrow\"><span id=\"MathJax-Span-2283\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-303\" style=\"display: none;\">m</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2284\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2285\" class=\"mrow\"><span id=\"MathJax-Span-2286\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-304\" style=\"display: none;\">n</code>"},"solution":"None of the above.","pass":true},{"seed":71300962,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":"\\frac{1}{8}","MULTIPLIER":8,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2449\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2450\" class=\"mrow\"><span id=\"MathJax-Span-2451\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-327\" style=\"display: none;\">m</code> varies directly with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2452\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2453\" class=\"mrow\"><span id=\"MathJax-Span-2454\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-328\" style=\"display: none;\">n</code>"},"solution":"\\frac{m}{n} = 8","pass":true},{"seed":216613767,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":"\\frac{1}{3}","MULTIPLIER":3,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2605\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-2606\" class=\"mrow\"><span id=\"MathJax-Span-2607\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-351\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2608\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-2609\" class=\"mrow\"><span id=\"MathJax-Span-2610\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-352\" style=\"display: none;\">y</code> vary directly"},"solution":"None of the above.","pass":true},{"seed":125777435,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":"\\frac{1}{8}","MULTIPLIER":8,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2761\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2762\" class=\"mrow\"><span id=\"MathJax-Span-2763\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-375\" style=\"display: none;\">m</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2764\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2765\" class=\"mrow\"><span id=\"MathJax-Span-2766\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-376\" style=\"display: none;\">n</code> are in direct variation"},"solution":"\\frac{m}{n} = 8","pass":true},{"seed":56668171,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":"\\frac{1}{2}","MULTIPLIER":2,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2917\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2918\" class=\"mrow\"><span id=\"MathJax-Span-2919\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-399\" style=\"display: none;\">m</code> is directly proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-2920\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-2921\" class=\"mrow\"><span id=\"MathJax-Span-2922\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-400\" style=\"display: none;\">n</code>"},"solution":"\\frac{m}{n} = 2","pass":true},{"seed":24697914,"type":"v1-over-v2","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":3,"MULTIPLIER":"\\frac{1}{3}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3073\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-3074\" class=\"mrow\"><span id=\"MathJax-Span-3075\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-423\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3076\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-3077\" class=\"mrow\"><span id=\"MathJax-Span-3078\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-424\" style=\"display: none;\">y</code> are in direct variation"},"solution":"\\frac{x}{y} = \\frac{1}{3}","pass":true},{"seed":132879902,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3403\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-3404\" class=\"mrow\"><span id=\"MathJax-Span-3405\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-469\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3406\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-3407\" class=\"mrow\"><span id=\"MathJax-Span-3408\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-470\" style=\"display: none;\">y</code> are in direct variation"},"solution":"\\frac{1}{7} \\cdot x = y","pass":true},{"seed":229265523,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":8,"MULTIPLIER":"\\frac{1}{8}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3565\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-3566\" class=\"mrow\"><span id=\"MathJax-Span-3567\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-491\" style=\"display: none;\">a</code> varies directly with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3568\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-3569\" class=\"mrow\"><span id=\"MathJax-Span-3570\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-492\" style=\"display: none;\">b</code>"},"solution":"None of the above.","pass":true},{"seed":262307599,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3727\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-3728\" class=\"mrow\"><span id=\"MathJax-Span-3729\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-513\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3730\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-3731\" class=\"mrow\"><span id=\"MathJax-Span-3732\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-514\" style=\"display: none;\">b</code> are in direct variation"},"solution":"\\frac{1}{7} \\cdot a = b","pass":true},{"seed":45364134,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":3,"MULTIPLIER":"\\frac{1}{3}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3889\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-3890\" class=\"mrow\"><span id=\"MathJax-Span-3891\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-535\" style=\"display: none;\">m</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-3892\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-3893\" class=\"mrow\"><span id=\"MathJax-Span-3894\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-536\" style=\"display: none;\">n</code> are in direct variation"},"solution":"\\frac{1}{3} \\cdot m = n","pass":true},{"seed":187196466,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":4,"MULTIPLIER":"\\frac{1}{4}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4051\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-4052\" class=\"mrow\"><span id=\"MathJax-Span-4053\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-557\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4054\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-4055\" class=\"mrow\"><span id=\"MathJax-Span-4056\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-558\" style=\"display: none;\">b</code> are in direct variation"},"solution":"None of the above.","pass":true},{"seed":28793126,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4213\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-4214\" class=\"mrow\"><span id=\"MathJax-Span-4215\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-579\" style=\"display: none;\">x</code> varies directly with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4216\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-4217\" class=\"mrow\"><span id=\"MathJax-Span-4218\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-580\" style=\"display: none;\">y</code>"},"solution":"None of the above.","pass":true},{"seed":67093639,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":2,"MULTIPLIER":"\\frac{1}{2}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4375\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-4376\" class=\"mrow\"><span id=\"MathJax-Span-4377\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-601\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4378\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-4379\" class=\"mrow\"><span id=\"MathJax-Span-4380\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-602\" style=\"display: none;\">b</code> vary directly"},"solution":"\\frac{1}{2} \\cdot a = b","pass":true},{"seed":195289671,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":"\\frac{1}{7}","MULTIPLIER":7,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4537\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-4538\" class=\"mrow\"><span id=\"MathJax-Span-4539\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-623\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4540\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-4541\" class=\"mrow\"><span id=\"MathJax-Span-4542\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-624\" style=\"display: none;\">b</code> vary directly"},"solution":"None of the above.","pass":true},{"seed":94148769,"type":"inverse-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4695\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-4696\" class=\"mrow\"><span id=\"MathJax-Span-4697\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-645\" style=\"display: none;\">m</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4698\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-4699\" class=\"mrow\"><span id=\"MathJax-Span-4700\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-646\" style=\"display: none;\">n</code> vary directly"},"solution":"\\frac{1}{7} \\cdot m = n","pass":true},{"seed":150259976,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":4,"MULTIPLIER":"\\frac{1}{4}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4857\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-4858\" class=\"mrow\"><span id=\"MathJax-Span-4859\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-667\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-4860\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-4861\" class=\"mrow\"><span id=\"MathJax-Span-4862\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-668\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"a = \\frac{1}{4} \\cdot \\frac{1}{b}","pass":true},{"seed":246030896,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":3,"MULTIPLIER_INVERSE":3,"MULTIPLIER":"\\frac{1}{3}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5040\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-5041\" class=\"mrow\"><span id=\"MathJax-Span-5042\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-688\" style=\"display: none;\">x</code> is inversely proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5043\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-5044\" class=\"mrow\"><span id=\"MathJax-Span-5045\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-689\" style=\"display: none;\">y</code>"},"solution":"x = \\frac{1}{3} \\cdot \\frac{1}{y}","pass":true},{"seed":171846650,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":9,"MULTIPLIER_INVERSE":"\\frac{1}{9}","MULTIPLIER":9,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5223\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-5224\" class=\"mrow\"><span id=\"MathJax-Span-5225\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-709\" style=\"display: none;\">m</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5226\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-5227\" class=\"mrow\"><span id=\"MathJax-Span-5228\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-710\" style=\"display: none;\">n</code>"},"solution":"m = 9 \\cdot \\frac{1}{n}","pass":true},{"seed":31798715,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":"\\frac{1}{2}","MULTIPLIER":2,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5396\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-5397\" class=\"mrow\"><span id=\"MathJax-Span-5398\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-730\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5399\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-5400\" class=\"mrow\"><span id=\"MathJax-Span-5401\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-731\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"a = 2 \\cdot \\frac{1}{b}","pass":true},{"seed":165199039,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":"\\frac{1}{7}","MULTIPLIER":7,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5569\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-5570\" class=\"mrow\"><span id=\"MathJax-Span-5571\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-751\" style=\"display: none;\">x</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5572\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-5573\" class=\"mrow\"><span id=\"MathJax-Span-5574\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-752\" style=\"display: none;\">y</code>"},"solution":"x = 7 \\cdot \\frac{1}{y}","pass":true},{"seed":160694589,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":4,"MULTIPLIER":"\\frac{1}{4}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5742\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-5743\" class=\"mrow\"><span id=\"MathJax-Span-5744\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-772\" style=\"display: none;\">m</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5745\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-5746\" class=\"mrow\"><span id=\"MathJax-Span-5747\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-773\" style=\"display: none;\">n</code> are in inverse variation"},"solution":"m = \\frac{1}{4} \\cdot \\frac{1}{n}","pass":true},{"seed":260223645,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":4,"MULTIPLIER":"\\frac{1}{4}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5925\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-5926\" class=\"mrow\"><span id=\"MathJax-Span-5927\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-793\" style=\"display: none;\">a</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-5928\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-5929\" class=\"mrow\"><span id=\"MathJax-Span-5930\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-794\" style=\"display: none;\">b</code>"},"solution":"a = \\frac{1}{4} \\cdot \\frac{1}{b}","pass":true},{"seed":28492926,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":4,"MULTIPLIER_INVERSE":"\\frac{1}{4}","MULTIPLIER":4,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6108\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-6109\" class=\"mrow\"><span id=\"MathJax-Span-6110\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-814\" style=\"display: none;\">m</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6111\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-6112\" class=\"mrow\"><span id=\"MathJax-Span-6113\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-815\" style=\"display: none;\">n</code>"},"solution":"m = 4 \\cdot \\frac{1}{n}","pass":true},{"seed":8685431,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":"\\frac{1}{7}","MULTIPLIER":7,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6281\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-6282\" class=\"mrow\"><span id=\"MathJax-Span-6283\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-835\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6284\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-6285\" class=\"mrow\"><span id=\"MathJax-Span-6286\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-836\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"None of the above.","pass":true},{"seed":42845782,"type":"inverse-variation","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":"\\frac{1}{7}","MULTIPLIER":7,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6454\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-6455\" class=\"mrow\"><span id=\"MathJax-Span-6456\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-856\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6457\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-6458\" class=\"mrow\"><span id=\"MathJax-Span-6459\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-857\" style=\"display: none;\">y</code> vary inversely"},"solution":"x = 7 \\cdot \\frac{1}{y}","pass":true},{"seed":86218512,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6627\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-6628\" class=\"mrow\"><span id=\"MathJax-Span-6629\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-877\" style=\"display: none;\">a</code> is inversely proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6630\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-6631\" class=\"mrow\"><span id=\"MathJax-Span-6632\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-878\" style=\"display: none;\">b</code>"},"solution":"a \\cdot b = \\frac{1}{6}","pass":true},{"seed":256089925,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6800\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-6801\" class=\"mrow\"><span id=\"MathJax-Span-6802\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-902\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-6803\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-6804\" class=\"mrow\"><span id=\"MathJax-Span-6805\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-903\" style=\"display: none;\">y</code> are in inverse variation"},"solution":"x \\cdot y = \\frac{1}{6}","pass":true},{"seed":15279421,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":5,"MULTIPLIER_INVERSE":"\\frac{1}{5}","MULTIPLIER":5,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7146\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-7147\" class=\"mrow\"><span id=\"MathJax-Span-7148\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-952\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7149\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-7150\" class=\"mrow\"><span id=\"MathJax-Span-7151\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-953\" style=\"display: none;\">y</code> vary inversely"},"solution":"x \\cdot y = 5","pass":true},{"seed":181093817,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":2,"MULTIPLIER_INVERSE":"\\frac{1}{2}","MULTIPLIER":2,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7309\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-7310\" class=\"mrow\"><span id=\"MathJax-Span-7311\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-977\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7312\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-7313\" class=\"mrow\"><span id=\"MathJax-Span-7314\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-978\" style=\"display: none;\">b</code> vary inversely"},"solution":"a \\cdot b = 2","pass":true},{"seed":253642798,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":"\\frac{1}{8}","MULTIPLIER":8,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7472\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-7473\" class=\"mrow\"><span id=\"MathJax-Span-7474\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1002\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7475\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-7476\" class=\"mrow\"><span id=\"MathJax-Span-7477\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1003\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"a \\cdot b = 8","pass":true},{"seed":263497540,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7635\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-7636\" class=\"mrow\"><span id=\"MathJax-Span-7637\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1027\" style=\"display: none;\">a</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7638\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-7639\" class=\"mrow\"><span id=\"MathJax-Span-7640\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1028\" style=\"display: none;\">b</code>"},"solution":"a \\cdot b = \\frac{1}{7}","pass":true},{"seed":184171043,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7808\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-7809\" class=\"mrow\"><span id=\"MathJax-Span-7810\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1052\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7811\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-7812\" class=\"mrow\"><span id=\"MathJax-Span-7813\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1053\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"None of the above.","pass":true},{"seed":257739880,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":8,"MULTIPLIER":"\\frac{1}{8}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7981\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-7982\" class=\"mrow\"><span id=\"MathJax-Span-7983\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1077\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-7984\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-7985\" class=\"mrow\"><span id=\"MathJax-Span-7986\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1078\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"a \\cdot b = \\frac{1}{8}","pass":true},{"seed":222731322,"type":"v1-v2-over-k","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":8,"MULTIPLIER_INVERSE":8,"MULTIPLIER":"\\frac{1}{8}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8154\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-8155\" class=\"mrow\"><span id=\"MathJax-Span-8156\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1102\" style=\"display: none;\">x</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8157\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-8158\" class=\"mrow\"><span id=\"MathJax-Span-8159\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-1103\" style=\"display: none;\">y</code>"},"solution":"x \\cdot y = \\frac{1}{8}","pass":true},{"seed":230740528,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8327\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-8328\" class=\"mrow\"><span id=\"MathJax-Span-8329\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1127\" style=\"display: none;\">m</code> is inversely proportional to <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8330\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-8331\" class=\"mrow\"><span id=\"MathJax-Span-8332\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1128\" style=\"display: none;\">n</code>"},"solution":"\\frac{1}{6} \\cdot \\frac{1}{m} = n","pass":true},{"seed":2072790,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"x","V2":"y","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8518\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.615em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.396em, 1000em, 2.241em, -0.582em);\"><span id=\"MathJax-Span-8519\" class=\"mrow\"><span id=\"MathJax-Span-8520\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.047em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0078.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.53em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1152\" style=\"display: none;\">x</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8521\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.426em, -0.595em);\"><span id=\"MathJax-Span-8522\" class=\"mrow\"><span id=\"MathJax-Span-8523\" class=\"mi\"><img style=\"width: 7px; height: 9px; vertical-align: -3px; margin-right: -0.006em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0079.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.755em; vertical-align: -0.239em;\"></span></span></nobr></span><code id=\"MathJax-Element-1153\" style=\"display: none;\">y</code> are in inverse variation"},"solution":"\\frac{1}{6} \\cdot \\frac{1}{x} = y","pass":true},{"seed":106112457,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":9,"MULTIPLIER_INVERSE":9,"MULTIPLIER":"\\frac{1}{9}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8890\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-8891\" class=\"mrow\"><span id=\"MathJax-Span-8892\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1202\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-8893\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-8894\" class=\"mrow\"><span id=\"MathJax-Span-8895\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1203\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"\\frac{1}{9} \\cdot \\frac{1}{a} = b","pass":true},{"seed":24248966,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":"\\frac{1}{6}","MULTIPLIER":6,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9081\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-9082\" class=\"mrow\"><span id=\"MathJax-Span-9083\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1227\" style=\"display: none;\">m</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9084\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-9085\" class=\"mrow\"><span id=\"MathJax-Span-9086\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1228\" style=\"display: none;\">n</code> are in inverse variation"},"solution":"6 \\cdot \\frac{1}{m} = n","pass":true},{"seed":93860898,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":9,"MULTIPLIER_INVERSE":"\\frac{1}{9}","MULTIPLIER":9,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9262\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-9263\" class=\"mrow\"><span id=\"MathJax-Span-9264\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1252\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9265\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-9266\" class=\"mrow\"><span id=\"MathJax-Span-9267\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1253\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"9 \\cdot \\frac{1}{a} = b","pass":true},{"seed":98845402,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":5,"MULTIPLIER_INVERSE":5,"MULTIPLIER":"\\frac{1}{5}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9443\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-9444\" class=\"mrow\"><span id=\"MathJax-Span-9445\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1277\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9446\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-9447\" class=\"mrow\"><span id=\"MathJax-Span-9448\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1278\" style=\"display: none;\">b</code> vary inversely"},"solution":"\\frac{1}{5} \\cdot \\frac{1}{a} = b","pass":true},{"seed":60869574,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"m","V2":"n","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":7,"MULTIPLIER_INVERSE":7,"MULTIPLIER":"\\frac{1}{7}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9634\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.82em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-9635\" class=\"mrow\"><span id=\"MathJax-Span-9636\" class=\"mi\"><img style=\"width: 12px; height: 6px; margin-right: 0.02em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006D.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1302\" style=\"display: none;\">m</code> varies inversely with <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9637\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.547em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.397em, 1000em, 2.241em, -0.595em);\"><span id=\"MathJax-Span-9638\" class=\"mrow\"><span id=\"MathJax-Span-9639\" class=\"mi\"><img style=\"width: 8px; height: 6px; margin-right: 0.019em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/006E.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.528em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1303\" style=\"display: none;\">n</code>"},"solution":"\\frac{1}{7} \\cdot \\frac{1}{m} = n","pass":true},{"seed":795223,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":1,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":6,"MULTIPLIER":"\\frac{1}{6}","STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9825\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-9826\" class=\"mrow\"><span id=\"MathJax-Span-9827\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1327\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-9828\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-9829\" class=\"mrow\"><span id=\"MathJax-Span-9830\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1328\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"\\frac{1}{6} \\cdot \\frac{1}{a} = b","pass":true},{"seed":110985546,"type":"k-over-a","VARS":{"VARIABLE_NAMES":[["x","y"],["a","b"],["m","n"]],"V1":"a","V2":"b","MULTIPLIER_IS_FRACTIONAL":0,"MULTIPLIER_VALUE":6,"MULTIPLIER_INVERSE":"\\frac{1}{6}","MULTIPLIER":6,"STATEMENT":"<span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-10016\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.478em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.398em, 1000em, 2.24em, -0.583em);\"><span id=\"MathJax-Span-10017\" class=\"mrow\"><span id=\"MathJax-Span-10018\" class=\"mi\"><img style=\"width: 7px; height: 6px; margin-right: 0.022em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0061.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.526em; vertical-align: -0.012em;\"></span></span></nobr></span><code id=\"MathJax-Element-1352\" style=\"display: none;\">a</code> and <span style=\"\" aria-readonly=\"true\" role=\"textbox\" class=\"MathJax\"><nobr><span id=\"MathJax-Span-10019\" class=\"math\"><span style=\"display: inline-block; position: relative; width: 0.41em; height: 0pt; font-size: 122%;\"><span style=\"position: absolute; top: -2.025em; left: 0em; clip: rect(1.156em, 1000em, 2.241em, -0.578em);\"><span id=\"MathJax-Span-10020\" class=\"mrow\"><span id=\"MathJax-Span-10021\" class=\"mi\"><img style=\"width: 6px; height: 9px; margin-right: 0.007em;\" src=\"http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/png/Math/Italic/100/0062.png\"></span></span>&nbsp;<span style=\"display: inline-block; width: 0pt; height: 2.025em;\"></span></span></span><span style=\"border-left: 0em solid; display: inline-block; overflow: hidden; width: 0pt; height: 0.823em; vertical-align: -0.013em;\"></span></span></nobr></span><code id=\"MathJax-Element-1353\" style=\"display: none;\">b</code> are in inverse variation"},"solution":"6 \\cdot \\frac{1}{a} = b","pass":true}],"issues":6});